Problem: Which of these numbers is prime? ${14,\ 45,\ 61,\ 85,\ 99}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 14 are 1, 2, 7, and 14. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 61 are 1 and 61. The factors of 85 are 1, 5, 17, and 85. The factors of 99 are 1, 3, 9, 11, 33, and 99. Thus, 61 is a prime number.